On the distributions of scan statistics of a two-dimensional Poisson
Sven Erick Alm
In Advances in Applied Probability (SGSA) 29, 1-18 (1997).
Given a two-dimensional Poisson process, X, with intensity $\lambda$,
we are interested in the largest number of points, L, contained in a
translate of a fixed scanning set, C, restricted to lie inside a
The distribution of L is accurately approximated for rectangular
scanning sets, using a technique that can be extended to higher dimensions.
Reasonable approximations for non-rectangular scanning sets are also
obtained using a simple correction of the rectangular result.
Poisson process, scan statistic, approximation
Research supported by the Axel and Margaret Ax:son Johnson Foundation.